But for me I consider pushing music to the house to be a thing on its own and the TV to be a system worth its own setup. Mixing these can cost you.
So with that you look to some amplifier or receiver that has a few zones.
Then we have single source, and more noted at https://www.lifewire.com/home-music-system-overview-3134628 so you have to decide how far down the rabbit hole you will go.
By now you see there are far too many choices at this point and why answers are delayed or didn't happen. That out of the way. For the house music, there are multi zone models to peruse:
For the TV, it's a little easier but that odd 4 speaker setup may mean you have to add a speaker to hit 5.1 or other setups. There are plenty of receivers to choose from here.
our home is prewired with a blend of wall, ceiling, outdoor and floor speakers. I need input on a system to push the speakers for music. The room wired with (4) floor speakers may be used for TV